Tok mikropolarnog fluida

U ovom radu izučavamo model mikropolarnih fluida te pomoću zakona sačuvanja i uz dodatne pretpostavke poput izotropnosti, Fourierovog zakona, inkompresibilnosti izvodimo jednadžbe gibanja. Pokazuje se kako je taj model zapravo poopćena verzija klasičnog Navier-Stokesovog modela. Fizikalno gledajući, ovaj model je pogodan za fluide čije molekule se mogu rotirati neovisno o toku fluida i njegove lokalne vrtložnosti. Izvedeni model je analiziran u slučaju dva različita toka uz pripadne rubne uvjete. Za Poiseuille-ov i Couette-ov tok prikazan je utjecaj mikrorotacije na izvedeno egzaktno rješenje za brzinu i mikrorotaciju toka. Na samim rezultatima primjećuje se utjecaj karakterističnih geometrijskih veličina poput razmaka izmedu dviju ravnina kroz koje prolazi fluid. Utjecaj mikrostrukture fluida dolazi do izražaja kod malih geometrijskih dimenzija, gdje prevladavaju mirorotacijske sile i viskoznosti te tako utječu i na brzinu toka. Za šire kanale i slično, tok se može jednako dobro aproksimirati i klasičnim Navier-Stokesovim jednadžbama.In this work, we introduce the model of micropolar fluids. We derive equations of motion from conservation laws under a number of suplementary assumptions such as isotropy, Fourier’s law and incompressibility. It turns out that the micropolar fluid model represents a significant generalization of the classical, Navier-Stokes model. Physically, a micropolar model is suitable for fluids whose molecules can rotate independently of the fluid stream flow and its local vorticity. The derived model is considered for two different flows and various boundary conditions. For Poiseuille and Couette flow the influence of the microstructure on the exact solution for the velocity and microrotation is shown. One can conclude from the results that the characteristic geometrical dimension such as the distance beween the parallel planes has significant influence on the effective flow. Once these dimensions are small enough micropolar model is applicable, with the dominant microviscosities and microrotations the change is observed even in the velocity of the flow. For wider channels and such, the flow is quiet well described by the classical, Navier-Stokes equations